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# Career Choice and Wage Differentials

Career Choice and Wage Differentials. Same assignment as the one that you did.

Question 1 A

The Net Present Value of no college education, graduate and post graduate education should be compared within the type 1 person context and type 2 person context to find the choice with the highest NPV

Type 1 individual

The expected NPV of the college investment is calculated by subtracting the discounted cost of the type of education from the expected PV.

The Type one individual faces four possible scenarios once he begins working at age 18, 22 or 26. He could:

1. Work throughout the years 18,22 or 26 to 67= Probability is 0.28
2. Work till 28 then experience a 7-year career interruption at 28 that ends at 34 and then work till 67. Probability=0.42
3. Work till 35 and experience a career interruption that begins at 35 and ends at 41 then work from 42 to 67. Probability=0.12
4. Work till 28, experience a 14-year career interruption that lasts till age 41 then work from 42 to 67. Probability=0.18

N/B Since decisions are made at age 18; all cash inflows and outflows are discounted back to the year 18 which is year 0.

For a type 1 individual in the undergraduate track, we calculate the PV of the earnings after college education as follows:

Scenario A,

Individual works without interruption for 46 years has a PV earnings amount of:

PV= 30,000/(4.125-2.5) [1- [(1+2.5)/(1+4.125)]^46]

PV= \$950,717

Discounting this amount back to 18= 808,781

Scenario B

The work period is split into 3 periods:

Period 1: 22 to 67

PV= 30,000/(4.125-2.5) [1- [(1+2.5)/(1+4.125)]^6]

PV= 166,263

Discounting this amount back to 18= 141,441

Period 2: 28 to 34

Pre-interruption salary = 34,790

Salary at beginning of age 28= 31,311 (34,790*0.9)

PV at age 28= 31,311/(4.125-2.5) [1- [(1+2.5)/(1+4.125)]^7]

PV= 200,891

Discounting this amount back to 18= 134,094

Period 3: 35-67

Pre-interruption salary at beginning of age 35= 40,347

Salary at beginning of age 35= 36,312

PV at age 35= 36,312/(4.125-2.5) [1- [(1+2.5)/(1+4.125)]^33]

PV= 904,838

Discounting amount back to 18, =455,130

Total PV attributable to scenario B, discounted to age 18= 141,441+134,094+455,130

Total PV attributable to scenario B= 730, 665

Scenario C

Period 1= 22 to 34

PV= 30,000/(4.125-2.5) [1- [(1+2.5)/(1+4.125)]^13]

PV at age 22=341,409

PV discounted to 18= 290,439

Period 2: 35 to 41

Pre-interruption salary at 35=40,307

Salary at beginning of 35= 36,312

PV= 36,312/(4.125-2.5) [1- [(1+2.5)/(1+4.125)]^7]

PV at age 35= 232,978

PV discounted to 18= 117,187

Period 3: 42 to 67

Pre-interruption salary at 42= 49,158

Salary at 42= 44,242 (0.9*49,158)

PV= 44,242/(4.125-2.5) [1- [(1+2.5)/(1+4.125)]^26]

PV at age 42= 913,864

PV discounted to 18= 346,387

PV from scenario C discounted to age 18= 190,439+ 117,187+ 346,387

PV from scenario C =753,923

Scenario D

Period 1: 22 to 27

PV= 30,000/(4.125-2.5) [1- [(1+2.5)/(1+4.125)]^6]

PV at age 22=166,263

PV at age 18= 141,441

Period 2: 28 to 41

Pre-interruption salary = 34,790

Salary at beginning of age 28= 31,311 (34,790*0.9)

PV at age 28= 31,311/(4.125-2.5) [1- [(1+2.5)/(1+4.125)]^14]

PV at age 28= 380,838

PV at age 18= 254,209

Period 3: 42 to 67

Pre-interruption salary at 42= 49,158

Salary at 42= 39,326 (0.8*49,158)

PV= 39,326/(4.125-2.5) [1- [(1+2.5)/(1+4.125)]^26]

PV at year 42= 812,319

PV at age 18= 307,898

PV from scenario D at age 18= 307,898+ 141,441+254,209

PV from scenario D= 703,548

The cost of undergraduate education is a growing annuity from the university’s point of view.

PV= 35,000/(0.04125-0.1) [1- [(1+0.1)/(1+0.04125)]^4]

PV of the cost of college education= 146,267

Calculating the Expected PV:

EPV= 0.28*808,781+ 0.42*730,665+ 0.12*753,923+ 0.18*703,548

Expected PV of a type 1 individual from an undergraduate career track= 750,447

Expected NPV= 750,447-146,267

Expected NPV= 604,180

If the type 1 individual takes the doctoral track, the expected PV of his earnings can be calculated as follows:

Common Period/period 1

All doctoral students will work for years 26 and 27

PV= 50,000/(4.125-4.5) [1- [(1+4.5)/(1+4.125)]^14]

PV at 26= 96,211

PV at age 18= 69,628

Scenario A

Period 2: 28 to 67= P/(4.125-4.5) [1- [(1+4.5)/(1+4.125)]^40]

Payment at age 28= 54,601

PV at age 28= 2,251,772

PV at 18= 1,503,052

PV attributable to scenario A= (1,503,052 +69,628)

PV= 1,572,680

Scenario B

Payment at age 28= 0.75*54,601

P at age 28= 40,950

Period 2: 28 to 67

PV= 40,950/(4.125-4) [1- [(1+4)/(1+4.125)]^40]

PV at age 28= 1,536,838

Discounting to year 18, = 1,025,836

Total PV from scenario B=  (1,025,836 +69,628)

PV= 1,095,464

Scenario C

Period 2: 28 to 34

PV= 54,601/(4.125-4.5) [1- [(1+4.5)/(1+4.125)]^7]

PV at age 28= 371,055

PV at 18= 247,678

PV of earnings during and post interruption period, 35 to 67, 33 years:

PV= P/(4.125-4) [1- [(1+4)/(1+4.125)]^33]

Payment at beginning of year 35= 74,305*0.9

Payment= 66,875

PV at age 28= 2,079,239

PV at 18= 1,387,888

Total PV from scenario 3=  (1,387,888+69,628)

PV= 1,457,516

Scenario D

Payment at age 28= 0.75*54,601

P at age 28= 40,950

Period 2: 28 to 67

PV= 40,950/(4.125-4) [1- [(1+4)/(1+4.125)]^40]

PV at age 28= 1,536,838

Discounting to year 18, = 1,025,836

Total PV from scenario D=  (1,025,836 +69,628)

PV= 1,095,464

Calculating PV cost of a doctoral degree

C= 146,267+ PV of postgraduate education at age 18

PV= 75,000/(0.04125-0.15) [1- [(1+0.15)/(1+0.04125)]^4]

PV= 336,476

Discounted to age 18= 286,242

C= 146,267+ 286,242

C= 432,509

Calculating expected PV of a college education:

PV= 0.28 (1,572,680) + 0.42(1,095,464)+ 0.12 (1,457,516)+ 0.18(1,095,464)

PV= 440,350+ 460,095+ 174,902+ 197,184

PV= 1,272,531

NPV=1,272,531-432,509

NPV= 840,022

With the probability of career interruption, the type 1 individual should select the doctoral career track on the basis of the higher cash returns evidenced by the highest NPV of 840,022

Career Track for a Type 2 Person

To calculate the expected PV, the individual’s work life will be divided into two periods: pre and during 59 and post 59.

High school track

PV= 1.0 (PV pre 59) + 0.4 (PV post 59)

Pre-59 PV= P/(4.125-1.5) [1- [(1+1.5)/(1+4.125)]^42]

PV= 501,191

Post 59 PV at year 60= P/(4.125-1.5) [1- [(1+1.5)/(1+4.125)]^8]

Payment at age 60= 37,377

PV=263,070

Discounting the PV back to 18= 48,168

Expected earnings of type 2 individual from high school track

PV= 501191+0.6 (48,168)

PV= 530,092

NPV= 530,092

PV of earnings pre-59

PV= 30000/(4.125-2.5) *[1- [(1+2.5)/(1+4.125)]^38]

PV at 22= \$830,644

PV at 18= 706,635

PV of earnings between 60 and 67

Payment at 60= 76,670

PV= 76,670/(4.125-2.5) *[1- [(1+2.5)/(1+4.125)]^38]

PV at age 60= 557,870

PV discounted to year 18= 102,146

Expected PV earnings of type 2 individual from undergraduate track

PV= 706,635+ 0.6(102,146)

PV= 767,923

NPV= 767,923-146,267

NPV= \$621,656

Doctoral track

Pre-59 period

PV= 50,000/(4.125-4.5) *[1- [(1+4.5)/(1+4.125)]^34]

PV= 1,733,505

PV at 18= 1,254,541

Post-59 period

Payment at age 60= 223, 318

PV at age 60= 223,318/(4.125-4.5) *[1- [(1+4.5)/(1+4.125)]^8]

PV= 1,737,552

PV at 18= 318,146

Expected PV of earnings from a doctoral career track

PV= 1,254,541+ 0.6(318,146)

PV= 1,445,428

NPV= 1,445,428-432,509

NPV= 1,012,920

The doctoral career track has the highest NPV of  \$1,012,920. A type 2 individual choosing a career based on the monetary returns should select the doctoral track.

There will be a pay gap for the type 1 individual in any of the three career tracks and a type 2 individual in the similar career track at age 45. This is because the type 1 individual is very likely to experience at least one interruption during which his salary is lowered and will never recover to the point of the type 2 individual. The pay gap will continue after the type 1 individual resumes work for all the three tracks. It will however be widest for individuals in the high school track given that their salary did not grow during the interruption period. It will be narrowest for the undergraduate since their salaries are returned closer to their counterparts who had no interruption once the interruption is over.

At age 55, the pay gap for type 2 individuals still within their career and type 1 individuals with at least one career interruption will exist for all the three career tracks. The gap will be narrower for type 1 individuals in the undergraduate track with only one career interruption than it was at age 45 since they will be returned to 90% of what a type 2 individual earns at the end of the interruption.

Question 1 B.

Assuming only a late interruption, the individual is faced with scenario C of question A above:

Type 1 individual in undergraduate track:

Period 1: 22 to 34

PV= 30,000/(4.125-2.5) [1- [(1+2.5)/(1+4.125)]^13]

PV at age 22=341,409

PV at 18= 290,439

Period 2: 34 to 41

Pre-interruption salary at 35=40,307

Salary at beginning of 35= 36,312

PV= 36,312/(4.125-2.5) [1- [(1+2.5)/(1+4.125)]^7]

PV at age 35= 232,978

PV at 18= 117,187

Period 3: 42 to 67

Pre-interruption salary at 42= 49,158

Salary at 42= 44,242 (0.9*49,158)

PV at age 42= 913,864

PV at 18= 346,387

PV for undergraduate track= 290,439+117,187+ 346,387

PV= 754,013

NPV= 754,013-146,267

NPV= 607,746

NPV for type 1 individual in doctoral track:

Period 1: 26 and 27

PV= 50,000/(4.125-4.5) [1- [(1+4.5)/(1+4.125)]^14]

PV at 26= 96,211

PV at 18= 69,628

Period 2: 28 to 34

PV= 54,601/(4.125-4.5) [1- [(1+4.5)/(1+4.125)]^7]

PV at age 28= 371,055

PV at 18= 247,678

Period 3: 35 to 67

PV= P/(4.125-4) [1- [(1+4)/(1+4.125)]^33]

Payment at beginning of year 35= 74,305*0.9

Payment= 66,875

PV at age 35= 2,079,239

PV at 18= 1,045,849

Total PV at 18= 69,628+ 247,678+ 1,045,849

PV= 1,363,155

NPV= 1,363,156-432,509

NPV= 930,647

The NPV of type 1 individual in the high school career track is

Period 1: 18 to 28

PV= 20,000/(4.125-1.5) [1- [(1+1.5)/(1+4.125)]^7]

PV= 124,701

Period 2: 28 to 34

PV= 23,211/(4.125-1.5) [1- [(1+1.5)/(1+4.125)]^7]

PV at age 28= 144,723

PV at 18= 96,602

Period 3: 35 to 41 (interruption)

PV= P {[1-(1+r)^n]/r}

P at beginning of age 35= 0.75* 25,760

Payment during interruption= 19,320

PV at age 35= 115,426

PV at 18= 58,059

Period 4: 42 to 67

Pre-interruption salary=25,760

PV= 25,760/(4.125-1.5) [1- [(1+1.5)/(1+4.125)]^7]

PV at age 42=476,087

PV at 18= 148,959

PV discounted to age 18= 124,701+58,059+ 96,602+148,959Career Choice and Wage Differentials

PV= 428,321

NPV=428,321

The doctoral career track should be selected as it still presents the highest NPV of 930,647 for a type 1 individual.Career Choice and Wage Differentials

Type 2 individual

This individual is faced with only one scenario; work till 59.Career Choice and Wage Differentials

PV= 30000/(4.125-2.5) *[1- [(1+2.5)/(1+4.125)]^38]

PV= \$830,644

PV at 18= 706,635

NPV= 706,635-146,267

NPV= 560,368

Doctoral career track

PV= 50,000/(4.125-4.5) *[1- [(1+4.5)/(1+4.125)]^34]

PV= 1,733,505

PV at 18= 1,254,541

NPV= 1,254,541-432,509

NPV= 822,032

High school career track

PV between 18 and 59= P/(4.125-1.5) [1- [(1+1.5)/(1+4.125)]^42]

PV= 501,191

An individual with such a known career path should select the doctoral track, which provides the highest NPV

I expect a wage gap to exit between the type 1 individuals and the type 2 individual at age 45. This is because of the slower wage growth for type 1 individual during and following the interruption. At age 55 the type 2 individual receives zero wages and the wage gap is at the highest.

Question 2 A

The independent variable is schooling while the dependent is the wages. The average wages can be determined by substituting into the equation the mean value of education. After substitution we find that the mean wages for type M is 4087 while the mean wage for type F people is 3767 indicating a wage differential.

The explained wage differential is that arising from the schooling variable. An increase in one school year for a type F person results in a wage increase of 180 while the same results in a 210 wage increase for a type M person. The difference in education received by the Type M and Type F persons explains this differential. A large portion of the total wage differential is explained.Career Choice and Wage Differentials

There is an unexplained wage differential. For zero years of education, the type F person will receive a wage of 905, which is 10 higher than that received by a type M person with no education. A small portion of the wage differential is unexplained but it will become more significant as education years fall below the mean towards zero.Career Choice and Wage Differentials

Question 2 B

By substituting in the mean education and experience figures, the mean age for type M person is found to be 4,087 while that of the type F person is 4,429.5.

It appears that Type M people receive education that is better paid by employers as compared to type F people. An increase in education years by one increases the Type M person’s wage by 60 while the same results in an increase by 50 for a type F person. The career track of Type F people values experience more than that of type M people with additional experience by one year resulting in a wage increase of 125. This is 5 higher than what a type M person would receive for an additional year of experience.Career Choice and Wage Differentials

For people above the mean age and experience, the wage differential is deeper while the differential diminishes to the unexplained differential as a result of the difference in interval coefficients as mean age and experience reduce further below the mean. The difference in the intercept values indicates the unexplained wage differential. The unexplained wage differential portion is significantly large and is biased against the type M person. The type F person with zero education and zero experience will earn 405. This is 254 more than what a type M person at the same level earns. C. Smith and Smythe’s conclusions will agree that pay discrimination exists but will disagree as to the extent of the discrimination. Smith will also conclude that majority of the wage differential is explained with only a small portion being unexplained while Smythe will find that the unexplained portion of the wage differential is larger and probably significant. I expect the researchers to arrive at a consensus since they will recognize that addition of the experience variable causes a change in the model with some of the explaining power of the education variable being reduced.

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